F(x)=2x2+18x-14

Solution for F(x)=2x2+18x-14 equation:

(F)=2F^2+18F-14

We move all terms to the left:

(F)-(2F^2+18F-14)=0

We get rid of parentheses

-2F^2+F-18F+14=0

We add all the numbers together, and all the variables

-2F^2-17F+14=0

a = -2; b = -17; c = +14;
Δ = b2-4ac
Δ = -172-4·(-2)·14
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{401}}{2*-2}=\frac{17-\sqrt{401}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{401}}{2*-2}=\frac{17+\sqrt{401}}{-4}
$